Elastocaloric, barocaloric and magnetocaloric effects in spin crossover polymer composite films

Giant barocaloric effects were recently reported for spin-crossover materials. The volume change in these materials suggests that the transition can be influenced by uniaxial stress, and give rise to giant elastocaloric properties. However, no measurements of the elastocaloric properties in these compounds have been reported so far. Here, we demonstrated the existence of elastocaloric effects associated with the spin-crossover transition. We dissolved particles of ([Fe(L)2](BF4)2, [L=2,6di(pyrazol-1-yl)pyridine]) into a polymeric matrix. We showed that the application of tensile uniaxial stress to a composite film resulted in a significant elastocaloric effect. The elastocaloric effect in this compound required lower applied stress than for other prototype elastocaloric materials. Additionally, this phenomenon occurred for low values of strain, leading to coefficient of performance of the material being one order of magnitude larger than that of other elastocaloric materials. We believe that spin-crossover materials are a good alternative to be implemented in eco-friendly refrigerators based on elastocaloric effects.


Entropy curves
The combination of specific heat data with the pressure-dependent thermal curves enables the determination of the entropy, referenced to a value at a given temperature (T 0 ) and atmospheric pressure, as: where T 1 and T 2 are the start and end temperatures the SCO transition.C LS p and C HS p are specific heats of the LS and HS states, respectively, and where x is the fraction of the sample in the LS state.Equation ( 1) is computed by assuming pressure-independent specific heats, which is a good approximation, taking into account the relatively narrow temperature interval over which it is computed.Nevertheless, the contribution to the entropy (∆S + (T 0 , p)) arising from the thermal expansion of each phase cannot be neglected for compressible organic and metal-organic materials.Such a contribution can be computed as: with ∆p = (p − p atm ) ≃ p, and where ∂V ∂T p is evaluated at p atm = 1 atm, and it is assumed to be pressureindependent.
The entropy curves as a function of temperature for selected values of applied pressure are finally computed as: S(T, p) = S ′ (T, p) + ∆S + (T 0 , p)

Model
We use a two-dimensional Ginzburg-Landau model to study an inclusion exhibiting a volumetric phase transition embedded into an elastic matrix.The free energy density is written as an expansion in terms of the so-called symmetry-adapted strains, which are linear combinations of components of the Lagrangian strain tensor, ε ij .These are the volumetric, e 1 = (ε xx + ε yy )/ √ 2, deviatoric, e 2 = (ε xx − ε yy )/ √ 2 and shear, e 3 = ε xy , strains.The order parameter of the phase transformation is the volumetric strain, e 1 .Thus, within the inclusion the free energy density is expanded in terms of this symmetry-adapted strain up to fourth order, which is the lowest order required to model a first-order phase transition.We also include the quadratic terms on the non order parameter strain components, e 2 and e 3 , which are essential to properly model the long range anisotropic elastic interactions.Finally, a gradient term for each symmetry-adapted strain is also included.For simplicity, other gradient terms of the same order that symmetry allows are neglected.Thus, the free energy density within the inclusion is written as where T is the temperature and T c is the stability limit of the high temperature phase.A, ζ and γ are related to second and higher order elastic constants of the inclusion, and κ n represent a contribution to the energy cost of creating variations in the symmetry-adapted strains.
The free energy density of the matrix, which is purely elastic with no phase transition, is simply written as The parameter A 1 is the bulk modulus A 1 = C 11 + C 12 .The parameters A 2 and A 3 are related to the secondorder elastic constants C ′ and C 44 : A 2 = C 11 − C 12 = 2C ′ and A 3 = 4C 44 .For simplicity we simulate an isotropic system and thus we use the relationship A 3 = 2A 2 .The symmetry-adapted strains are computed from the Lagrangian strain tensor which, in turn, is obtained from the displacement field, u(r), which is the variable of the model.The total free energy of the system thus reads, with where Ω is the volume containing the inclusion and Ω is the volume of the system excluding the inclusion., where e 1 is the transformation strain and Ω is the volume of the inclusion.Circles correspond to circular inclusions and squares correspond to square inclusions.Dashed lines are linear fits to the numerical data.For a given shape and size of the inclusion, the total free energy is minimized at T = 0.8 T c , below the phase transition, and the resulting strain fields are analyzed.For both circular and square inclusions it is obtained that the strain within the inclusion is almost homogeneous.Thus, the free energy of the inclusion can be approximated to, as, due to strain compatibility, the non order parameters are negligibly small if the gradient of the order parameter is small.In Fig. S14 we plot the free energy of the matrix vs e 2 1 Ω, where e 1 is the average value of the volumetric strain within the inclusion.We obtain a linear relationship for both circular and square inclusions, although the proportionality constant is different in these two cases.A slight deviation from linearity is attributed to the finite size of the matrix in the simulations.
Thus, the free energy of the matrix can be approximated as, where B is a constant that depends on the bulk modulus of the matrix and on the shape of the inclusion.This energy cost leads to a decrease in the transition temperature of the inclusion, in agreement with experimental findings.
The parameters of the model T c , A, and κ 1 are fixed to unity which defines reduced units of energy, length and temperature.In these reduced units the parameters of the model used to study the free energy of the matrix are ζ = 20, γ = 5000, A 1 = 0.05, A 2 = 0.1, A 3 = 0.2 and κ 2 = κ 3 = 1.The simulations have been carried out in a system of size L × L = 1000 × 1000 reduced units of length discretized onto a 512 × 512 mesh, and the radius of the circular inclusions considered was R = 20, 39, 59 and 78 reduced units of length.

Figure S4 :Figure
Figure S4: Characteristics of pure PVC film.(a) differential scanning calorimetry, (b) isofield magnetization measured at 1 T and (c) stress-induced elastocaloric isothermal entropy change for selected values of applied uniaxial tensile stress.In all measurements, PVC shows no transformation.
e n s i t y ( c o u n t s )

Figure
Figure S7: X-ray diffraction (XRD) measurements of 1/PVC.The measurements at room temperature (a, black curve) and at 200 K (b, red curve) show diffraction peaks of 1 on top of a PVC background.As only a small fraction of 1 transforms during cooling, both XRD measurements are very similar.Small peaks next to the main peaks (see inset in b) belong to the transforming fraction.

Figure S8 :Figure S9 :Figure S10 :
Figure S8: Scanning Electron Microscopy (SEM) image of 1/PVC showing small SCO particles dispersed in the polymer matrix.The image was taken at an acceleration voltage of 5 kV using secondary electrons.

Figure S11 :Figure S12 :
FigureS11: Magnetocaloric isothermal entropy change corresponding to the application of a (a) 1 T, (b) 3 T and (c) 5 T magnetic field for 1 (black symbols and lines) and 1/PVC (red symbols and lines).Open symbols correspond to decreasing temperatures, while solid symbols correspond increasing temperatures.Lines are guides to the eye.

Figure S14 :
Figure S14: Free energy of the elastic matrix upon transformation of a single isolated inclusion vs e 21 Ω, where e 1 is the transformation strain and Ω is the volume of the inclusion.Circles correspond to circular inclusions and squares correspond to square inclusions.Dashed lines are linear fits to the numerical data.